I am actually not sure if gif's and siggy size are what is causing all the crashes. Database and server error 500 means what exactly? We really need a Computer geek to weigh in here.
I can try to help explain the basics

(although I don't often work with servers and large databases, so if someone is a bigger computer geek than I, please correct me if I'm wrong!).
A fairly official explanation of an error 500 is can be found here:
http://www.checkupdown.com/status/E500.html
This basically says, a number of things could have gone wrong, but it's all on the server side meaning that it has nothing to do with your computer or your internet connection. Super helpful, right? From what I've read from Goofy Moe's fundraising posts and other posts around the forum, it sounds like there are a couple of issues that are probably causing the server to crash.
1. Too many members for the number of servers DPF has For every member that is logged in and making a request (ie viewing a new thread, submitting a post, changing profile details), the server has to deal with it. A server can only process one request at a time. All requests except for the one that is currently being processed are put into a queue to wait. Most requests do not take too long to process, so it is usually not very noticeable that you've been waiting. But the server can only have so many requests in the queue at once. Once that queue reaches it's capacity, the server cannot process any incoming requests until it has more room in the queue. It will continue to crash for people until it has processed some requests. The big problem comes when it processes one request and then gets 10 more and then processes 1 request and gets 10 more etc, so it seems like the site is just completely down because only one of those requests can actually get through.
The best solution to this problem is to get more servers to handle the number of requests coming in. A good temporary solution is, as other people have mentioned, fewer gifs and smaller signatures (both in pixel size and byte size) as this will make pages faster to load and will allow the server to get to a new request that much faster.
2. The database is reaching its limits A database holds many things. In the case of DPF it holds everyone's profile information, all the posts within a thread, all the threads within the forum and all the information associated with each of these things. As you can imagine, that's a lot of information! Text is cheap. A single character only takes up 1-2 bytes depending on how it is encoded. But images are costly, and videos even more so (1kb is equal to 1024 bytes). This is why when you upload an image or a video to a post, it asks for a URL. The images and videos are actually being stored in another website's database so that the only thing taking up room in DPF's database is the text for the URL. (At least, I believe that is how images are being handled...) Even though text takes up a small amount of space, the database is still limited. It can only hold a finite amount and once we get closer and closer to reaching that amount, two things happen. First, there is more information to sort through so it is harder for the server to find what it is looking for. This causes a request to take longer to process and eventually the queue will get too long and the server will crash. Second, if new information is put into a database that doesn't have a lot of storage space it gets harder and harder to find places to put that data. This isn't as immediate of a problem, but it is still a problem.
The best solution to this is to get a bigger and better database, or maybe even multiple databases to hold different pieces of information (this is typically what big websites like Amazon do to make things more efficient). But until we can do that, image size (this time just the byte size) is what will help. It seems that all sigpics are stored in the database, which is why both images from URLs and images from your computer are limited to 125kb. The forum software automatically changes the image for you so that it is under 125kb (if your signature looks pixelated, the computer simplified your image to make the byte size smaller). But if you can get it under 125 kb, every little bit helps!
Every website is run differently on the back end, so this might not be 100% accurate as to how DPF works. But hopefully all of that makes sense and will answer some questions on people's minds.